Get a sheet of new shutter curtain cloth. Shutter curtain cloth is e.g. available at micro-tools.com (they have offices in California and in Germany and ship worldwide).

Insert the folded metal sheets into the new curtains. Close them with a small hammer. Be careful and hammer from both sides as you will bend it slightly in the direction where the hammer comes from.

Sadly, this way the ends of the sheets will have no pressure and don't hold the strips on the curtain as good as they did originally. A drop of glue might solve this problem. It is not as bad if you use a lowered spring tension when putting the shutter back together as I did (see step 8).